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This book provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal, and is suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science.
Ear Decompositions of Matching Covered Graphs
It is shown that every nonbipartite matching covered graph has a canonical ear decomposition which is optimal, that is one which has as few double ears as possible.
On a Conjecture of Lovász Concerning Bricks: I. The Characteristic of a Matching Covered Graph
The notion of the characteristic of a separating cut in a matching covered graph is introduced and some basic properties are established to first prove the theorem for solid bricks, that is, bricks which do not have any nontrivial separating cuts.
Extremal critically connected matroids
- U. Murty
- MathematicsDiscret. Math.
- 1 March 1974
On a Conjecture of Lovász Concerning Bricks: II. Bricks of Finite Characteristic
Here, it is established the existence of suitable separating cuts in nonsolid bricks and the theorem is proved by applying induction to cut-contractions with respect to such cuts.
The perfect matching polytope and solid bricks